To be thick-skinned is to not be bothered by criticism and rejection. When you're thick-skinned, you're mentally tough.
It can help you to remember the meaning of this term if you think about it literally. Someone with thick, tough, rough skin isn't going to be hurt by a little pinch or paper cut, unlike someone with thin skin. So thick-skinned people are also unaffected by less physical harms, like being criticized, rejected, or turned down. If you're thick-skinned, you don't let failure or disappointment get you down: you keep believing in yourself and moving forward.